Bones are deforming the mesh at different rates. Is there a way to fix this?
This is because the eyelashes are not included in the head bone's vertex group :


Select the armature and switch to pose mode
Select the head mesh and switch to weight painting mode
Select the head bone and you'll see that :




You just have to paint the whole head mesh vertices for the head bone's vertex group with the same weight color, including the eyelashes, and you'll be saved !